Finite Group Databasebeta

← #11783838

Subgroups — #11783838

Order 1152.

442 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64287C211yesmaximal, characteristic
2#10593824C211yesmaximal, characteristic
3#10593738C212yesmaximal, complemented
4#10592439C211yesmaximal, characteristic
5#10590156C212yesmaximal, complemented
6C2×#3830C2211yescharacteristic
7C2×#3792C411yescharacteristic, complemented
8C2×#3792C2212yes—
9C2×#3792C2211yescharacteristic
10C22×#622C411yescharacteristic, complemented
11C22×#622C2211yescharacteristic
12#64287—22no—
13#64287—22no—
14C2×#3788C411yescharacteristic, complemented
15C2×#3787C411yescharacteristic, complemented
16#64086C2212yes—
17#63788C412yescomplemented
18#63780C412yescomplemented
19#63777—22no—
20C4×#622—22no—
21C32×#99C411yescharacteristic
22#63661C411yescharacteristic
23#63633C412yes—
24#4740—62no—
25C2×C32×D4C2×C411yescharacteristic
26C2×#638C2×C411yescharacteristic
27C2×#638C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30#3830—22no—
31#3830—22no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×#634C2×C411yescharacteristic
34#3792—22no—
35#3792—22no—
36#3792—22no—
37#3792C2×C414yes—
38C2×#622—22no—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622C2×C411yescharacteristic
42C2×#622C2×C411yescharacteristic
43C2×#622C2×C411yescharacteristic
44C2×#622C2×C411yescharacteristic
45C2×#622D412yes—
46C2×#622D412yes—
47#3788—22no—
48#3787—21no—
49#3787—21no—
50C32×C22⋊C4C2×C412yes—
51#3757C2×C412yes—
52#3750—22no—
53C4×C3⋊Dic3—22no—
54#1757—91nomaximal, Sylow
55C2×#237—62no—
56#877—64no—
57C3×#99—22no—
58#834—62no—
59#806—64no—
60C23×C32C4211yescharacteristic
61C23×C32C22×C411yescharacteristic
62C22×C3⋊D3C4211yescharacteristic
63C32×D4—22no—
64C2×C32×C4—22no—
65C2×C32×C4C4211yescharacteristic
66#638—22no—
67#638—22no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C4211yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3#4112yes—
76C4×C3⋊D3—21no—
77C4×C3⋊D3—21no—
78#634—22no—
79#622—21no—
80#622—21no—
81#622—24no—
82#622C22⋊C411yescharacteristic
83#622C22⋊C411yescharacteristic
84#622C22⋊C412yes—
85C2×#131—91no—
86#413—91no—
87#410—91no—
88#405—92no—
89#344—92no—
90C2×C3×D4—22no—
91C2×#67—62no—
92C2×#67—62no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95#237—124no—
96#237—124no—
97C2×C4×D3—62no—
98C2×Dic6—62no—
99C3×C22⋊C4—24no—
100#217—64no—
101Dic3⋊C4—124no—
102C4×Dic3—124no—
103C22×C32—21no—
104C22×C32—41no—
105C22×C32—41no—
106C22×C32C2×C4211yescharacteristic
107C22×C32C4×D412yes—
108C2×C3⋊D3—21no—
109C2×C3⋊D3—41no—
110C32×C4—21no—
111C32×C4—42no—
112C3⋊Dic3—21no—
113C3⋊Dic3—42no—
114C3⋊Dic3C2×C22⋊C411yescharacteristic
115C3⋊Dic3#11711yescharacteristic
116C3⋊Dic3C4×D412yes—
117C2×#41—91no—
118#131—182no—
119#131—182no—
120C2×M16—91no—
121C2×M16—91no—
122C2×M16—91no—
123C2×M16—92no—
124C22×C8—91no—
125C22×C8—91no—
126C22×C8—91no—
127#117—92no—
128#101—92no—
129#100—92no—
130#99—91no—
131#99—92no—
132#99#15711yescharacteristic
133#97—182no—
134C4×C8—182no—
135C23×C3—22no—
136C23×C3—22no—
137C22×D3—62no—
138C3×D4—44no—
139C2×C3×C4—22no—
140C2×C3×C4—44no—
141#67—124no—
142#67—124no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—64no—
146C2×Dic3—64no—
147C2×Dic3—62no—
148C2×Dic3—122no—
149C2×Dic3—122no—
150C2×Dic3—124no—
151C4×D3—122no—
152C4×D3—122no—
153Dic6—124no—
154C2×C32—22no—
155C2×C32—21no—
156C2×C32—41no—
157C2×C32C4×C22⋊C411yescharacteristic
158C3⋊D3—41no—
159#41—182no—
160#41—182no—
161C2×Q8—91no—
162C2×D4—91no—
163C2×D4—91no—
164C2×D4C2×#15711yescharacteristic
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168M16—94no—
169M16—182no—
170M16—182no—
171M16—182no—
172M16—182no—
173C2×C8—92no—
174C2×C8—92no—
175C2×C8—91no—
176C2×C8—91no—
177C2×C8—91no—
178C2×C8—91no—
179C2×C8—181no—
180C2×C8—181no—
181C2×C8—181no—
182C2×C8—181no—
183C2×C8—182no—
184C4⋊C4—182no—
185C22⋊C4—92no—
186C22⋊C4C2×#15712yes—
187C42—182no—
188C22×C3—22no—
189C22×C3—24no—
190C22×C3—42no—
191C22×C3—82no—
192C22×C3—82no—
193C2×D3—122no—
194C2×D3—242no—
195C3×C4—42no—
196C3×C4—84no—
197Dic3—64no—
198Dic3—62no—
199Dic3—62no—
200Dic3—122no—
201Dic3—244no—
202C32#175711yescharacteristic, complemented, Sylow
203C23—91no—
204C23C4×#15711yescharacteristic
205C23C22×#15711yescharacteristic
206Q8—182no—
207D4—22no—
208D4—182no—
209D4—182no—
210C2×C4—22no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—92no—
215C2×C4—91no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—181no—
220C2×C4—182no—
221C2×C4C4×#15711yescharacteristic
222C8—91no—
223C8—91no—
224C8—92no—
225C8—181no—
226C8—181no—
227C8—184no—
228C2×C3—22no—
229C2×C3—44no—
230C2×C3—42no—
231C2×C3—82no—
232D3—242no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—181no—
237C22—361no—
238C22C2×C4×#15711yescharacteristic
239C22D4×#15712yes—
240C4—21no—
241C4—42no—
242C4—91no—
243C4—92no—
244C4—91no—
245C4—181no—
246C4—362no—
247C3—22no—
248C2—22no—
249C2—21no—
250C2—41no—
251C2—361no—
252C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC2C22⋊C4×#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC32×#99C4
socleC2×C32C4×C22⋊C4
prime radicalC2×#3830C22
cosocleC22×C3⋊Dic3C23
hypercenter#99#157
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #10593738C2semidirect
5. #10590156C2semidirect
7. C2×#3792C4semidirect
10. C22×#622C4semidirect
14. C2×#3788C4semidirect
15. C2×#3787C4semidirect
17. #63788C4semidirect
18. #63780C4semidirect
202. C32#1757semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#642872
#105938242
#105937382
#105924392
#105901562
#17579